First you find the mean of the data set, which is 7. Then to find standard deviation you have to follow the formula which tells you to subtract the mean from each number under the square root : √(2 - 7)^2 + (9 - 7)^2 + (10 - 7)^2 + (4 - 7)^2 + (8 - 7)^2 + (4 - 7)^2 + (12 - 7). Once you solve the parenthesis you square it, once you square it the negatives won't matter. That will leave you with this : √(25 + 4 + 9 + 9 + 25). The formula tells you to find the sum of those numbers (which is 72) then subtract one from how many numbers there are, 5 - 1 = 4, and divide your sum by that number. So 72 / 4 = 18. Then you find the square root of 18 and that becomes your answer.
